Volume 65, pp. 326-346, 2026.

A new stable and inversion-free iteration for computing the matrix square root of large and sparse matrices

Li Zhu, Feng Wu, Keqi Ye, Yuelin Zhao, Jiqiang Hu, and Wanxie Zhong

Abstract

The objective of this research is to compute the principal matrix square root using a sparse approximation. A new stable inversion-free iteration (SIFI) is presented. An analysis of the sparsity and error of the matrices involved in the iterative process is given. Based on the bandwidth and error analysis, a more efficient algorithm combining the SIFI with a filtering technique is proposed. The computational efficiency and accuracy of the proposed method are demonstrated through the computation of the principal square root of various matrices, confirming its superiority over existing approaches.

Full Text (PDF) [540 KB], BibTeX , DOI: 10.1553/etna_vol65s326

Key words

matrix square root, iterative algorithm, error analysis, bandwidth analysis

AMS subject classifications

65F45, 65F10, 65F35

Links to the cited ETNA articles

[6]	Vol. 28 (2007-2008), pp. 16-39 Michele Benzi and Nader Razouk: Decay bounds and $O$($n$) algorithms for approximating functions of sparse matrices